Two uniform spherical stars made of same material have radii `R` and `2R`. Mass of the smaller planet is `m`. They start moving from rest towards each from a large distance under mutual force of gravity. The collision between the starts is inelastic with coefficient of restitution `1//2`.
The maximum separation between their centres after their first collision

Options

A. `4R`
B. `6R`
C. `8R`
D. `12 R`

Answer

a

Explanation

Let maximum separation is `r` from conservation of energy
`U_(i)+K_(i)=U_(f)+K_(f)`
`-(G(m)(8m))/(3R)+2/3(Gm^(2))/R-=(G(m)(8m))/r+0`
`-(8Gm^(2))/(3R)+2/3(Gm^(2))/R=(-8)/r`
`8/r=6/3 R`
`r=4R`